The laws of adopting a child born of a surrogate mother are very complex in California. I cannot speak to the relevant laws in Vietnam. I have changed your question to indicate the focus on adoption law, since many adoption attorneys are more familiar with these questions.
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Adoption laws are very complicated and have many layers. Not all immigration attorneys are engaged in this practice. You need very specific experience to do that. For initial information please visit www.adoption.state.us.gov. Seek out an immigration attorney with that specific experience and make a consultation. You will save yourself A LOT OF HASSLE later on.
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This area of law is emerging and changing. You'll almost certainly want to get several opinions before you go forward any further...
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